Difference between Independent and Dependent Events in Probability

In probability theory, independent events and dependent events are two key concepts that determine the likelihood of certain outcomes. Here are the main differences between these two types of events:

Independent Events:

Independent events are events where the outcome of one event does not affect the outcome of the other. In other words, the occurrence of one event does not influence the probability of the other event happening. For example, flipping a coin and rolling a die are independent events.

Dependent Events:

Dependent events are events where the outcome of one event does affect the outcome of the other. In this case, the probability of the second event is influenced by the outcome of the first event. For example, drawing two cards from a deck without replacement is a dependent event.

Understanding the difference between independent and dependent events is crucial in probability theory as it helps in calculating the overall probability of multiple events occurring in a sequence or simultaneously.